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Q. No.Given below are two statements:
Statement I:
The magnetic field due to a segment \({d\vec l}\) of a current-carrying wire carrying a current, \(I\) is given by:
\({d\vec B}=\dfrac{\mu_0}{4\pi}~I\left({d\vec l}\times\dfrac{\vec r}{r^3}\right ),\)
where \(\vec{r}\) is the position vector of the field point with respect to the wire segment.
Statement II:
The magnetic field of a current-carrying wire is never parallel to the wire.
1.
Statement I and Statement II are True and Statement I is the correct explanation of Statement II.
2.
Statement I and Statement II are True and Statement I is not the correct explanation of Statement II.
3.
Statement I is True, and Statement II is False.
4.
Statement I is False, and Statement II is True.
\({d\vec B}=\dfrac{\mu_0}{4\pi}~I\left({d\vec l}\times\dfrac{\vec r}{r^3}\right ),\)
where \(\vec{r}\) is the position vector of the field point with respect to the wire segment.
Subtopic: Biot-Savart Law |
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A wire carrying a current \(I_0\) oriented along the vector \(\big(3\hat{i}+4\hat{j}\big)\) experiences a force per unit length of \(\big(4F\hat{i}-3F\hat{j}-F\hat{k}\big).\) The magnetic field \(\vec{ B}\) equals:
1. \(\dfrac{F}{I_0}\left(\hat{i}+\hat{j}\right)\)
2. \(\dfrac{5F}{I_0}\left(\hat{i}+\hat{j}+\hat{k}\right)\)
3. \(\dfrac{F}{I_0}\left(\hat{i}+\hat{j}+\hat{k}\right)\)
4. \(\dfrac{5F}{I_0}\hat{k}\)
Subtopic: Lorentz Force |
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Two current carrying loops of wire are placed as shown in the figure, the inner loop \((P)\) having a radius \((r)\) which is much smaller than the radius \((R)\) of the outer loop \((Q)\). Both the loops are concentric, but the currents in one case are in the same sense while in the other, in the opposite sense.
In both cases, the torque on \(P\) due to \(Q\) is zero. If \(P\) is slightly rotated about a diameter, then, it will return to its initial position in:
In both cases, the torque on \(P\) due to \(Q\) is zero. If \(P\) is slightly rotated about a diameter, then, it will return to its initial position in:
| 1. | case (I) but not in case (II). |
| 2. | case (II) but not in case (I). |
| 3. | both cases (I) and (II). |
| 4. | neither of cases (I) and (II). |
Subtopic: Magnetic Moment |
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Identical cells are connected to identical square wire loops as shown in the two diagrams, and the magnetic fields are respectively \(B_1\) and \(B_2\) at the centres.
Then, we can conclude that:
1. \(B_1>0, B_2=0\)
2. \(B_1> B_2>0\)
3. \(B_2> B_1>0\)
4. \(B_1=0, B_2=0\)
Then, we can conclude that:
1. \(B_1>0, B_2=0\)
2. \(B_1> B_2>0\)
3. \(B_2> B_1>0\)
4. \(B_1=0, B_2=0\)
Subtopic: Biot-Savart Law |
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Two long straight wires carrying currents \(i_1, i_2\) are placed as shown in the figure, just avoiding contact. The separation between the wires is negligible, and the wires are aligned along \(x\) & \(y\) axes respectively.
The wire along the \(x\text-\)axis experiences:
The wire along the \(x\text-\)axis experiences:
| 1. | a force along \(+y\) axis only. |
| 2. | a force along \(-y\) axis. |
| 3. | zero force, but a torque. |
| 4. | no force and no torque. |
Subtopic: Force between Current Carrying Wires |
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Given below are two statements:
| Assertion (A): | Work done by magnetic force on a charged particle moving in a uniform magnetic field is zero. |
| Reason (R): | Path of a charged particle in a uniform magnetic field, projected in the direction of field, will be a straight line. |
| 1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
| 3. | (A) is true but (R) is false. |
| 4. | Both (A) and (R) are false. |
Subtopic: Lorentz Force |
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The same current \(I\) is flowing in two infinitely long wires in the positive \(x \) and \(y\)-directions. The magnetic field at a point \((0,0,a)\) would be:
| 1. | \( \dfrac{\mu_{0} i}{2 \pi a}(\hat{i}+\hat{j})\) | 2. | \( \dfrac{\mu_{0} i}{2 \pi a}(-\hat{i}+\hat{j})\) |
| 3. | \(\dfrac{\mu_{0} i}{2 \pi a}(-\hat{i}-\hat{j})\) | 4. | \(\dfrac{\mu_{0} i}{2 \pi a}(\hat{i}-\hat{j})\) |
Subtopic: Biot-Savart Law |
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A current-carrying loop has a magnetic moment \(\vec{M}\) and carries a current \(I.\) The loop is placed in a uniform magnetic field \(\vec{B}.\) What is the magnitude of torque acting on the loop if the plane of the loop makes an angle of \(60^\circ\) with the direction of the magnetic field?
1. \(MB~ \text{cos} 60^\circ\)
2. \(MB~ \text{sin} 60^\circ\)
3. \(MB~ \text{tan} 60^\circ\)
4. \(MB~ \text{cot} 60^\circ\)
1. \(MB~ \text{cos} 60^\circ\)
2. \(MB~ \text{sin} 60^\circ\)
3. \(MB~ \text{tan} 60^\circ\)
4. \(MB~ \text{cot} 60^\circ\)
Subtopic: Current Carrying Loop: Force & Torque |
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Which of the following statements about a moving coil galvanometer is incorrect?
| 1. | The spring in a galvanometer provides a counter torque that balances the magnetic torque. |
| 2. | A galvanometer has multiple turns of wire to enhance the torque acting on the coil. |
| 3. | In all positions, the magnetic field \(B\) remains parallel to the plane of the coil. |
| 4. | The deflection \(\phi\) indicated by the scale is proportional to the square of the current flowing through the coil. |
Subtopic: Moving Coil Galvanometer |
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As shown in the figure, the equal current \(I\) flows in the two segments; the magnetic field at the centre of the loop due to segment \(ABC\) is \(B_1\) and due to segment \(ADB\) is \(B_2.\) Then:
1. \(B_1 > B_2\)
2. \(B_1 < B_2\)
3. \(B_1=B_2\)
4. \(2B_1=B_2\)
1. \(B_1 > B_2\)
2. \(B_1 < B_2\)
3. \(B_1=B_2\)
4. \(2B_1=B_2\)
Subtopic: Biot-Savart Law |
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